Question

A positron has a mass of 9.11 x 10^-31 kg, and charge qp = +e = +1.60 x 10^-19 C. It is moving towards an α particle (qα = +2e, mα = 6.66 x 10^-27 kg) with a speed of 3.00 x 10^6 m/s. At this instant the separation between the two is 2.00 x 10^-10 m. Assume α particle stays at rest. (a) Calculate the speed of positron at 1.00 x 10^-10 m from α particle. (b) What is the separation between the two when positron comes to rest?

Answer 1

To find the speed of the positron at a certain distance from the alpha particle and the separation distance when the positron comes to rest.

Step-by-step explanation:

The speed of a positron at a certain distance from an α particle can be found using the conservation of energy. At 1.00 x 10^-10 m from the α particle, the positron's kinetic energy will be equal to the potential energy at that distance. Using this information, we can calculate the speed of the positron as it approaches the α particle.

To find the separation between the two when the positron comes to rest, we can set the final kinetic energy of the positron equal to zero and solve for the separation distance. This will give us the point at which the positron stops moving towards the α particle.

Answer 2

Part a)

`v = 2.25 * 10^6 m/s`

Part b)

`r = 0.72 * 10^(-10) m`

Step-by-step explanation:

As we know that alpha particle remain at rest always so the energy of system of positron and alpha particle will remain constant

So we will have

`(kq_1q_2)/(r_1) + (1)/(2)mv_1^2 = (kq_1q_2)/(r_2) + (1)/(2)mv_2^2`

here we know that

`q_1 = 1.6 * 10^(-19) C`

`q_2 = 2(1.6 * 10^(-19)) C`

also we have

`r_1 = 2.00 * 10^(-10) m`

`r_2 = 1.00 * 10^(-10) m`

`v_1 = 3.00 * 10^6 m/s`

`m = 9.11 * 10^(-31) kg`

now from above equation we have

`2.304 * 10^(-18) + 4.0995* 10^(-18) = 4.608 * 10^(-18) + (1)/(2)(9.11 * 10^(-31))v^2`

`v = 2.25 * 10^6 m/s`

Part b)

Now when it come to rest then again by energy conservation we can say

`(kq_1q_2)/(r_1) + (1)/(2)mv_1^2 = (kq_1q_2)/(r_2) + (1)/(2)mv_2^2`

now here final speed will be zero

`2.304 * 10^(-18) + 4.0995* 10^(-18) = ((9/times 10^9)(1.6* 10^(-19))(2* 1.6 * 10^(-19)))/(r_2)`

`r = 0.72 * 10^(-10) m`